Earlier this year, we had some electricians do some work on the house, and when they did, they installed a new ceiling light fixture (including a new box). Unfortunately, they left a hole in the ceiling adjacent to where the box ended up. The deepest part is about 3/4" deep and 3.5" square, but the damage to the ceiling covers about a 6" square area in total.
Here's a version of the picture with the three different surfaces within the hole highlighted and detailed:
Obviously, I'd like to patch it, but I can't figure out the right way to do it. I tried affixing an adhesive patch kit to the slats around the hole, but the adhesive wouldn't hold. I tried drilling into what I thought was solid wood at the base of the hole—turns out it was just some sort of smaller wood piece, not secure enough to anchor anything into.
How should I go about patching this hole up? I'm a very novice DIYer when it comes home stuff, so basic steps are greatly appreciated.